开口曲线上混合解析函数的Riemann边值问题  

Riemann boundary value problems for mixed analytic functions on the open curve

作　　者：王路路 刘华[1] WANG Lulu;LIU Hua(School of Science,Tianjin University of Technology and Education,Tianjin 300222)

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《宁夏师范学院学报》2020年第10期33-40,共8页Journal of Ningxia Normal University

摘　　要：引入混合解析函数并讨论其Riemann-Hilbert型边值问题.先建立混合解析函数的Plemelj公式和Cauchy型积分.在此基础上研究Cauchy积分在开口曲线端点处的性质以及开口曲线上混合解析函数的边值问题,继而讨论混合解析函数Riemann边值问题的可解条件,并在有解时给出解的封闭形式.The notion of mixed analytic functions is introduced and it′s Riemann-Hilbert boundary value problems are discussed in this article.First,the Plemelj formula and Cauchy integral of the mixed analytic function are established.Based on above,the properties of the Cauchy integral at the endpoints and interior of the open curve are considered respectively.Finally,the solvable conditions and the closed form of solutions of Riemann boundary value problems for the mixed analytic function on the open curve are studied.

关 键 词：混合解析函数 PLEMELJ公式 RIEMANN边值问题 

分 类 号：O174.5[理学—数学]